Not common in the West, but Asian cultures (e.g. India) may salt tea and coffee. It does act in that way (though ideally the coffee should have been better prepared in the first place) - add it like sugar, and add to taste.

Incidentally, let me tell you about the time that I was in Kashmir and some crazy old muslim guy took me around the old town all day; introduced me to all of his friends; took me to the mosque so that I could stand in defence of the West in fleeting arguments as we moved from group to group; invited me back to his home, where his bizarrely enthusiastic (in the Indian hand-holding, innocently bro-love sense that is slightly awkward in the West) son showed me his watercolor paintings and argued metaphysics and global politics; (all this, he hinted lated in the night, because it was ramadan and he was discharging an islamic duty to infidels, and that he loathed me as being such ...); and then finally served heavily salted tea ... well salted tea was just too much, and I bailed the fuck out the next morning.

It may work, but it may be more effective to dial in your coffee brewing. Bitterness comes from over extraction, either through too high a brew temp, too fine a grind, too high a coffee to water ratio, or too long a contact time between coffee and water.

Correctly brewed coffee won't have any bitterness. For the easiest and least likely to be bitter method, I highly recommend the Chemex. The filters are much thicker and make it easy to avoid bitterness and the chemex has a wide margin of error.